The weight of frogs in grams in a marsh population are normally distributed with unknown mean (μ) and standard deviation (σ) = 1.25 grams. What is the probability that the mean () of a random sample of 4 frogs lies within one gram of the true mean (μ)? Round your answer to three decimal places.

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Answer to a math question The weight of frogs in grams in a marsh population are normally distributed with unknown mean (μ) and standard deviation (σ) = 1.25 grams. What is the probability that the mean () of a random sample of 4 frogs lies within one gram of the true mean (μ)? Round your answer to three decimal places.

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P(\mu -1 < \bar{X} < \mu +1)

=P(\bar{X} < \mu+1) -P(\bar{X}< \mu-1)

=P\left(\frac{\bar{X}-\mu}{\sigma /\sqrt{n}} < \frac{\mu+1-\mu}{1.25/\sqrt{4}}\right)-P\left(\frac{\bar{X}-\mu}{\sigma /\sqrt{n}} < \frac{\mu-1-\mu}{1.25/\sqrt{4}}\right)

=P(Z < 1.6)-P(Z < -1.6)

=0.9452-0.0548

=0.8904

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